Well-posedness of the water-wave with viscosity problem

被引：3

作者：

Granero-Belinchon, Rafael ^{[1
]}

Scrobogna, Stefano ^{[2
]}

机构：

[1] Univ Cantabria, Dept Matemat Estadist & Comp, Santander, Spain

[2] Univ Seville, Dept Anal Matemat, Seville, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 276卷

基金：

欧洲研究理事会;

关键词：

Damped water waves; Viscosity; Well-posedness; Cross-diffusion system; FREE-SURFACE FLOWS; FLUID LAYER; MODEL;

D O I：

10.1016/j.jde.2020.12.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability in Sobolev spaces for arbitrary dissipation. On the other hand, we establish the global well-posedness in Wiener spaces for a sufficiently large viscosity. These results are the first rigorous proofs of well-posedness for the Dias, Dyachenko & Zakharov system (Physics Letters A 2008) modeling gravity waves with viscosity when surface tension is not taken into account. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：96 / 148

页数：53

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